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High Order Numerical Methods for the Dynamic SGS Model of Turbulent Flows with Shocks

Part of: Partial differential equations, initial value and time-dependent initial-boundary value problems Computer aspects of numerical algorithms

Published online by Cambridge University Press:  01 February 2016

D. V. Kotov ,
H. C. Yee ,
A. A. Wray ,
A. Hadjadj  and
B. Sjögreen
D. V. Kotov
Affiliation:
Bay Area Environmental Research Institute, 625 2nd St. Ste 209, Petaluma, CA, USA
H. C. Yee*
Affiliation:
NASA-Ames Research Center, Moffett Field, CA94035, USA
A. A. Wray
Affiliation:
NASA-Ames Research Center, Moffett Field, CA94035, USA
A. Hadjadj
Affiliation:
CORIA UMR 6614 & INSA de Rouen, 76800 St-Etienne du Rouvray, France
B. Sjögreen
Affiliation:
Computational Scientist, Lawrence Livermore National Laboratory, USA
*
*Corresponding author. Email addresses:[email protected] (D. V. Kotov), [email protected] (H. C. Yee), [email protected] (A. A. Wray), [email protected] (A. Hadjadj), Sjö[email protected] (B. Sjögreen)
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Abstract

Simulation of turbulent flows with shocks employing subgrid-scale (SGS) filtering may encounter a loss of accuracy in the vicinity of a shock. This paper addresses the accuracy improvement of LES of turbulent flows in two ways: (a) from the SGS model standpoint and (b) from the numerical method improvement standpoint. In an internal report, Kotov et al. ( “High Order Numerical Methods for large eddy simulation (LES) of Turbulent Flows with Shocks”, CTR Tech Brief, Oct. 2014, Stanford University), we performed a preliminary comparative study of different approaches to reduce the loss of accuracy within the framework of the dynamic Germano SGS model. The high order low dissipative method of Yee & Sjögreen (2009) using local flow sensors to control the amount of numerical dissipation where needed is used for the LES simulation. The considered improved dynamics model approaches include applying the one-sided SGS test filter of Sagaut & Germano (2005) and/or disabling the SGS terms at the shock location. For Mach 1.5 and 3 canonical shock-turbulence interaction problems, both of these approaches show a similar accuracy improvement to that of the full use of the SGS terms. The present study focuses on a five levels of grid refinement study to obtain the reference direct numerical simulation (DNS) solution for additional LES SGS comparison and approaches. One of the numerical accuracy improvements included here applies Harten's subcell resolution procedure to locate and sharpen the shock, and uses a one-sided test filter at the grid points adjacent to the exact shock location.

Keywords

High order numerical methodsturbulent flows with shocksGermano SGS modelLES

MSC classification

Secondary: 65Z05: Applications to physics 65M06: Finite difference methods 65M50: Mesh generation and refinement 65M55: Multigrid methods; domain decomposition 65M60: Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods 65M99: None of the above, but in this section 65Y99: None of the above, but in this section
Type
Research Article
Information
Communications in Computational Physics , Volume 19 , Issue 2 , February 2016 , pp. 273 - 300
Copyright
Copyright © Global-Science Press 2016 

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